Problems in Geometry

Contents......Page 5
1. The Ratio and Proportionality of Line Segments, Similarity of Triangles......Page 7
2. Metric Relationships in a Right-Angled Triangle......Page 10
3. Regular Polygons, the Length of the Circumference and the Arc......Page 15
4. Areas of Plane Figures......Page 17
5. Solving Right-Angled Triangles......Page 22
Law of Cosines......Page 29
Law of Sines......Page 31
Areas of Triangles, Parallelograms and Quadrilaterals......Page 32
Particular Cases of Solving Oblique Triangles......Page 34
Heron's Formula......Page 35
Radii r and R of Inscribed and Circumscribed Circles and the Area S of a Triangle......Page 36
Miscellaneous Problems......Page 37
7. Basic Concepts and Axioms. Two Straight Lines in Space......Page 43
8. Straight Lines Perpendicular and Inclined to a Plane......Page 46
9. Angles Formed by a Straight Line and a Plane......Page 52
10. Parallelism of a Straight Line and a Plane......Page 55
11. Parallel Planes......Page 59
12. Dihedral Angles. Perpendicular Planes......Page 63
13. Areas of Projections of Plane Figures......Page 67
14. Polyhedral Angles......Page 69
15. Prisms and Parallelepipeds......Page 71
16. The Pyramid......Page 77
17. The Truncated Pyramid......Page 81
18. Regular Polyhedrons......Page 84
19. The Right Circular Cylinder......Page 86
20. The Right Circular Cone......Page 89
21. The Truncated Cone......Page 93
22. Areas of Parallelepipeds and Prisms......Page 97
23. Areas of Pyramids......Page 102
24. Areas of Truncated Pyramids......Page 105
25. Areas of Cylinders......Page 108
26. Areas of Cones......Page 111
27. Areas of Truncated Cones......Page 115
28. Volumes of Parallelepipeds......Page 118
29. Volumes of Prisms......Page 122
30. Volumes of Pyramids......Page 127
31. Volumes of Truncated Pyramids......Page 133
32. Volumes of Cylinders......Page 137
33. Volumes of Cones......Page 141
34. Volumes of Truncated Cones......Page 145
35. Spheres......Page 149
36. Areas of Spheres and Their Parts......Page 152
37. Volumes of Spheres and Their Parts......Page 155
38. Inscribed and Circumscribed Spheres......Page 159
39. Polyhedrons......Page 164
40. Round Solids......Page 168
41. Areas and Volumes of Prisms......Page 172
42. Areas and Volumes of Pyramids......Page 176
43. Areas and Volumes of Round Solids......Page 181
Answers......Page 187